511
12
611
3655
Assumezto be0,2,4,6,8,10and find solution ofx+y=10−z, we getCase 1:z=0⇒x+y=10andx,y∈0,1,2,...,10This can be done in10+2C2=11C1ways.Case 2:z=2⇒x+y=8andx,y∈0,1,2,,8This can be done in8+2C2=9C1ways.Similarly, we can obtain for all the cases as7C1,5C1,3C1and1C1ways.The total number of solutions for the given expression is10+3C3=12C2ways.Hence, probability=11C1+9C1+7C1+5C1+3C1+1C112C2=3666=611Hence, option C is correct.